Advertisements
Advertisements
प्रश्न
Find the equation of a straight line with slope − 1/3 and y-intercept − 4.
Advertisements
उत्तर
Here, \[m = - \frac{1}{3}, c = - 4\]
Substituting the values of m and c in y = mx + c, we get,
\[y = - \frac{x}{3} - 4\]
\[ \Rightarrow x + 3y + 12 = 0\]
Hence, the equation of the straight line with slope
APPEARS IN
संबंधित प्रश्न
Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{2\pi}{3}\]
Find the slope of a line passing through the following point:
(3, −5), and (1, 2)
Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?
The slope of a line is double of the slope of another line. If tangents of the angle between them is \[\frac{1}{3}\],find the slopes of the other line.
Consider the following population and year graph:
Find the slope of the line AB and using it, find what will be the population in the year 2010.

Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).
Find the equation of a straight line with slope 2 and y-intercept 3 .
Find the equations of the bisectors of the angles between the coordinate axes.
Find the equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.
Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
Find the angles between the following pair of straight lines:
(m2 − mn) y = (mn + n2) x + n3 and (mn + m2) y = (mn − n2) x + m3.
If θ is the angle which the straight line joining the points (x1, y1) and (x2, y2) subtends at the origin, prove that \[\tan \theta = \frac{x_2 y_1 - x_1 y_2}{x_1 x_2 + y_1 y_2}\text { and } \cos \theta = \frac{x_1 x_2 + y_1 y_2}{\sqrt{{x_1}^2 + {y_1}^2}\sqrt{{x_2}^2 + {y_2}^2}}\].
Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text { is } \frac{2ab}{a^2 - b^2}\].
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
Find k, if the slope of one of the lines given by kx2 + 8xy + y2 = 0 exceeds the slope of the other by 6.
If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?
If x + y = k is normal to y2 = 12x, then k is ______.
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlock wise direction through an angle of 15°. Find the equation of the line in new position.
If the slope of a line passing through the point A(3, 2) is `3/4`, then find points on the line which are 5 units away from the point A.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.
Slope of a line which cuts off intercepts of equal lengths on the axes is ______.
The point (4, 1) undergoes the following two successive transformations:
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.
The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.
If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is ______.
